Figure 1 shows the influence of water on temperature dependence of logarithm of relative permittivity, ε′, and dielectric loss, ε″, of the nail plate at the selected frequency of 5 kHz. The release of about 9% of the water from the wet nail is manifested by ε′ and ε″ maxima near 100 °C. The curves for dry nail do not contain these peaks due to the lack of loosely bound water in this sample. Our previous dielectric studies of the human nail with about 11% water [4,5,6,7] also revealed the process of removing water, but at a lower temperature of 80 °C. Release of water in other α-keratin fibers using the DSC method [14,15,16,17] was also observed in a similar temperature range. In addition, plots for wet nail show that during the aging test for 1 h at 150 °C, the values of ε′ and ε″ are in the ranges 7.30–5.71 and 0.99–0.24, respectively. In the case of dry nail at 150 °C, the values of ε′ (5.64) and ε″ (0.22) are close to the values corresponding to the wet sample, indicating that this temperature is sufficient to release water from the nail plate. As in our previous dielectric studies on the animal horn  and nail , the results in Fig. 1 for wet samples are related to the interaction between water and polar surface groups such as OH, CO and NH keratin molecules, whereas these data for dry samples are attributed to the intermolecular interaction of the keratin inside the nail.
Figure 2 shows the frequency dependency ε′ and ε″ for wet and dry nails at 26, 36 and 45 °C referring, respectively, to the temperature before, during and above the physiological conditions. All these graphs in the full frequency range show that the dielectric parameters for wet samples are higher compared to dry samples. In other studies performed with the use of capacitive contact imaging  and electrical impedance spectroscopy , an increase in the dielectric properties of the nail was also observed along with the increase in the water content in this tissue. As a result of the presence of loosely bound water in a wet nail, two relaxation frequencies fc around 2 and 25 kHz (Fig. 2b), which are clearly visible in the case of dry nails, are masked due to joint movements between water molecules and polar active sites of keratin molecules. This overlapping effect of higher water content in the nail than in the presented paper on these two fc under physiological conditions also appeared in our earlier study . In contrast, for samples without water, the relaxation processes associated with the mobility of these polar active sites of keratin molecules and surrounding protons at 2 and 25 kHz occur on the surface and inside the nail tissue, respectively. In addition, in the range of 26–45 °C, for each frequency the values of ε′ and ε″ for wet nails increase, as compared to dry samples, for which both parameters are substantially unchanged. This indicates that the process of heating wet samples breaks hydrogen bonds formed by water on the surface of keratin molecules, which leads to a higher density of relaxing free polar groups and surrounding protons in comparison to dry samples. In the spectra shown in Fig. 2, the influence of water on dielectric behavior of nails is particularly visible below 2 kHz, where there is a low-frequency dispersion (LFD) in the form ε′ ~ f−n and ε″ ~ f−k with n and k in the range of 0.03–0.06 and 0.21–0.40, respectively. Dielectric studies of other authors regarding different biopolymers [19, 20] also showed the behavior of LFD in the α-dispersion region of the electric field used for these materials. To examine the differences between wet and dry nails, dielectric data from Fig. 2 are shown in Fig. 3 as a Cole–Cole representation. For the dry nail (Fig. 3a), two relaxation processes were obtained, from the semicircle fitting, one near 2 kHz, and the other near 25 kHz. In the case of wet nails (Fig. 3b), the semicircles reflect only one frequency of relaxation near 25 kHz, and then there is a continuous monotonic increase in both ε′ and ε″ with decreasing frequency, indicating that the Cole–Cole representation is inadequate.
As shown in Fig. 4, to characterize the dielectric properties of wet and dry nails above 2 kHz, data in Fig. 2 are expressed in the form of frequency dependencies of real and imaginary parts of the complex conductivity σ* (σ* = σ′ + jσ″), where σ′ and σ″ are given by σ′ = ωεoε″ and σ″ = ωεo(ε′ − εh), respectively, εo is the permittivity of a vacuum, ω is the angular frequency (ω = 2πf), and εh is the high-frequency limit of relative permittivity at 85 kHz. These results are an extension of the previous analysis of the complex permittivity ε* (ε* = ε′ −j ε″) for the nail using the Cole–Cole function , as well as the data shown in Fig. 3, to demonstrate that dielectric relaxation focused around 25 kHz really exists (Fig. 4b). Conductivity plots σ′ for wet nail at temperatures of 26, 36 and 45 °C in Fig. 4a are above the respective spectra for a dry nail. This behavior is confirmed by a higher conductivity increment Δσ′ on the order of 14–18 nS cm−1 for a wet sample in the range 2–85 kHz than Δσ′ of 6 nS cm−1 for a dry sample with a small change value of this parameter with increasing temperature. Because all these plots (Fig. 4a) are expressed by σ′ ~ fp with an exponent p between 0.8 and 1, in the range of 26–45 °C, the conduction of the proton jump is the dominant mechanism of the charge carrier flow. In addition, the fact that the relaxation time τ of protons for wet and dry nails depends on temperature up to 150 °C is confirmed in Arrhenius diagrams for τ, as shown in Fig. 5. The Arrhenius equation is an empirical equation that can provide information about energy consumed in a thermally activated process. Electrical conductivity is such a process. Because the conductivity in the nail refers to the charge, the equation Arrhenius with the Boltzmann constant (k) is used as τ = το exp (ΔH/kT), where το is the pre-exponential factor and ΔH is the activation energy. Fig 5 shows the plots as the natural logarithm of the relaxation time (ln τ) relative to the inverse of the temperature (T−1). The values of τ are calculated from the equation τ = εoε∞/σ , where ε∞ is the high-frequency limit of α-dispersion and σ is the steady-state conductivity. In our measurements from 22 to 150 °C, we have assumed the values of σ and ε∞ at 2 kHz and 85 kHz, respectively. The activation energy ΔH of the proton conduction obtained from the slope of the plots τ to ~ 100 °C for wet nails is in the range of 0.155–0.339 eV, and above this temperature for the dry nail, the value of ΔH is 0.182 eV. Correspondingly, values of τ decrease in the range 1.30–0.16 ms for a wet sample to ~ 100 °C and 3.20–1.65 ms for a dry sample above this temperature. On the other hand, the τ values increase in the range of 2.65–3.20 ms for a dry sample up to ~ 100 °C and 0.16–0.32 ms for a wet sample above this temperature. For comparison, in the range of 22–150 °C, the maximum and minimum τ values for a dry nail are 2.5 and 10 times longer, respectively, than the corresponding values τ for a wet nail. In addition, the obtained size Δσ′ (Fig. 4a) for both nail conditions is correlated with a relaxation process of approximately 25 kHz in the dielectric σ″ spectra for wet and dry materials in Fig. 4b, as a result of simultaneous occurrence of the conduction and polarization mechanism in this tissue. This behavior is confirmed in Fig. 6 as the variation of σ″ versus σ′ for wet and dry nails with clearly visible maximum values of σ″ for fc around 25 kHz. Thus, inside the wet and dry nails, the polarization mechanism originates from the orientational relaxation of the polar intermolecular groups with a relaxation time of τc = 0.006 ms (τc = 1/2πfc, fc = 25 kHz). This value τc is shorter compared to the relaxation time τ of the proton (Fig. 5), which changes with temperature. For example, at 22 °C, τc is about 217 and 442 times shorter than the corresponding τ for wet and dry nails. These results in Fig. 6 also show that the water content in the nail influences the maximum σ″ values at any temperature while maintaining a similar relaxation frequency fc. Therefore, such a stable fc value may facilitate the assessment of physiological changes in the affected nail plate, thus indicating potentially useful dielectric spectroscopy, as well as other techniques [22,23,24,25] in medical diagnosis or therapy.